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Ghella [55]
3 years ago
8

Alejandra's Tapas Bar offers a menu consisting of $9$ savory and $5$ sweet dishes. You can also get a mix-and-match plate consis

ting of two different dishes on the menu. How many different mix-and-match plates can you get consisting of two savory dishes?
Mathematics
1 answer:
Mariana [72]3 years ago
7 0

Answer:

45

Step-by-step explanation:

Given that the number of savory dishes is 9 and the number of sweet dished is 5.

Denoting all the 9 savory dishes by p_1, p_2,...,p_9, and all the sweet dishes by q_1,q_2,...,q_5.

The possible different mix-and-match plates consisting of two savory dishes are as follows:

There are 9 plates with q_1 from sweet plates which are (q_1, p_1), (q_1, p_2), ..., (q_1,p_9).

There are 9 plates with q_2 from sweet plates which are  (q_2, p_1), (q_2, p_2), ..., (q_2,p_9).

Similarly, there are 9 plated for each q_3, q_4 and q_5.

Hence, the total number of the different mix-and-match plates consisting of two savory dishes

= 9+9+9+9+9= 9\times5=45

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